Physics in Negative Curvature: Experiments on Hyperbolic Lattices with Superconducting Circuits.

Motivated by recent developments in hyperbolic band theory, hyperbolic metamaterials, and hyperbolic error correction codes, we present a novel way of realizing hyperbolic phenomena in the Poincaré disk model on a superconducting device. Our approach leverages high-Q resonators to resolve the fine details in the spectroscopy. Meanwhile, it mimics the non-uniform hyperbolic distance in the curved space electromagnetically by imposing variations in the capacitive couplings between resonators. We use this approach to experimentally realize a sublattice of the octagonal tiling of the Bolza surface. We also demonstrate, for the first time, an experimental realization of a hyperbolic lattice in a higher-genus Riemann surface (g=3). The experimental results are compared to numerical solutions predicted by hyperbolic band theory and the classical circuit simulations. Our approach furthers the study and simulation of physics in negatively curved spaces through synthetic means.